Handbook of Mathematical Fuzzy Logic

0372990 - ÚI 2012 RIV GB eng M - Monography Chapter
Hájek, Petr - Montagna, F. - Noguera, C.
Arithmetical Complexity of First-Order Fuzzy Logics. Chapter 11.
Handbook of Mathematical Fuzzy Logic. Vol. 2. London: College Publications, 2011 - (Cintula, P.; Hájek, P.; Noguera, C.), s. 853-908. Studies in Logic - Mathematical Logic and Foundations, 38. ISBN 978-1-84890-054-7
R&D Projects: GA ČR GEICC/08/E018; GA ČR GAP202/10/1826
Institutional research plan: CEZ:AV0Z10300504
Keywords : Arithmetical Complexity * First-Order Fuzzy Logics
Subject RIV: BA - General Mathematics

The main problem in this chapter is not whether a given predicate logic is decidable or not, but rather how undecidable it is, i.e. what is its undecidability degree. For the general semantics, the undecidability degrees are low. For the standard semantics, it depends: in the cases where we have standard completeness, like MTL or IMTL, the undecidability degrees are trivially as in the general semantics, in other cases, like Łukasiewicz first-order logic, the undecidability degrees are higher but still in the arithmetical hierarchy, while in product logic or in BL logic both tautologicity and satisfiability for the standard semantics fall outside the arithmetical hierarchy.
Permanent Link: http://hdl.handle.net/11104/0206171